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- Electron Transport in Bismuth at Liquid Helium Tempratures
- To obtain information on the band structure of bismuth, galvanomagnetic potentials were measured in a single crystal at liquid-helium and liquid-nitrogen temperatures. These measurements were analyzed for information on the different carriers, particularly for the existence of a high-mobility band of holes.
- The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes
- We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy.
- Oligonucleotide guanosine conjugated to gallium nitride nano-structures for photonics.
- In this work, I studied the hybrid system based on self-assembled guanosine crystal (SAGC) conjugated to wide-bandgap semiconductor gallium nitride (GaN). Guanosine is one of the four bases of DNA and has the lowest oxidation energy, which favors carrier transport. It also has large dipole moment. Guanosine molecules self-assemble to ribbon-like structure in confined space. GaN surface can have positive or negative polarity depending on whether the surface is Ga- or N-terminated. I studied SAGC in confined space between two electrodes. The current-voltage characteristics can be explained very well with the theory of metal-semiconductor-metal (MSM) structure. I-V curves also show strong rectification effect, which can be explained by the intrinsic polarization along the axis of ribbon-like structure of SAGC. GaN substrate property influences the properties of SAGC. So SAGC has semiconductor properties within the confined space up to 458nm. When the gap distance gets up to 484nm, the structure with guanosine shows resistance characteristics. The photocurrent measurements show that the bandgap of SAGC is about 3.3-3.4eV and affected by substrate properties. The MSM structure based on SAGC can be used as photodetector in UV region. Then I show that the periodic structure based on GaN and SAGC can have photonic bandgaps. The bandgap size and the band edges can be tuned by tuning lattice parameters. Light propagation and emission can be tuned by photonic crystals. So the hybrid photonic crystal can be potentially used to detect guanosine molecules. If guanosine molecules are used as functional linker to other biomolecules which usually absorb or emit light in blue to UV region, the hybrid photonic crystal can also be used to tune the coupling of light source to guanosine molecules, then to other biomolecules.
- Polymer Gels: Kinetics, Dynamics Studies and Their Applications as Biomaterials
- The polymer gels especially hydrogels have a very special structure and useful features such as unusual volume phase transition, compatibility with biological systems, and sensitivity to environmental stimuli (temperature, pH value, electric field, light and more), which lead to many potential applications in physical and biochemical fields. This research includes: (1) the theoretical and experimental studies of polymer gels on swelling kinetics, spinodal decomposition, and solution convection in gel matrix; (2) applications of polymer gels in wound dressing, tissue-simulating optical phantom and gel display. The kinetics of gel swelling has been theoretically analyzed by considering coupled motions of both solvent and polymer network. Analytical solutions of the solvent and the network movement are derived from collective diffusion equations for a long cylindrical and a large disk gel. Kinetics of spinodal decomposition of N-isopropylacrylamide (NIPA) polymer gel is investigated using turbidity and ultrasonic techniques. By probing movement of domains, a possible time-dependent gel structure in the spinodal decomposition region is presented. Theoretical studies of solution convection in gel matrix have been done and more analysis on dimensionless parameters is provided. To enhance the drug uptake and release capacity of silicone rubber (SR), NIPA hydrogel particles have been incorporated into a SR membrane. This SR/NIPA composite gel has promising attributes for wound dressing and other uses. Tissue-simulating optical phantom has been synthesized and studied using NIPA solution trapped inside a hydrogel. Polymer gels with engineered surface patterns were implemented. NIPA gel deposited on the surface of an acrylamide gel can be used as responsive gel display. A dynamically measurement technique of local shear modulus and swelling ratio of gel is presented based on an engineered periodic surface pattern as square array.
- Ballistic deposition: global scaling and local time series.
- Complexity can emerge from extremely simple rules. A paradigmatic example of this is the model of ballistic deposition (BD), a simple model of sedimentary rock growth. In two separate Problem-in-Lieu-of Thesis studies, BD was investigated numerically in (1+1)-D on a lattice. Both studies are combined in this document. For problem I, the global interface roughening (IR) process was studied in terms of effective scaling exponents for a generalized BD model. The model used incorporates a tunable parameter B to change the cooperation between aggregating particles. Scaling was found to depart increasingly from the predictions of Kardar-Parisi-Zhang theory both with decreasing system sizes and with increasing cooperation. For problem II, the local single column evolution during BD rock growth was studied via statistical analysis of time series. Connections were found between single column time series properties and the global IR process.
- Mechanism and the Effect of Microwave-Carbon Nanotube Interaction
- A series of experimental results about unusual heating of carbon nanotubes by microwaves is analyzed in this dissertation. Two of vibration types, cantilever type (one end is fixed and the other one end is free), the second type is both ends are fixed, have been studied by other people. A third type of forced vibration of carbon nanotubes under an alternating electromagnetic field is examined in this paper. Heating of carbon nanotubes (CNTs) by microwaves is described in terms of nonlinear dynamics of a vibrating nanotube. Results from the model provide a way to understand several observations that have been made. It is shown that transverse vibrations of CNTs during microwave irradiation can be attributed to transverse parametric resonance, as occurs in the analysis of Melde's experiment on forced longitudinal vibrations of a stretched elastic string. For many kinds of carbon nanotubes (SWNT, DWNT, MWNT, ropes and strands) the resonant parameters are found to be located in an unstable region of the parameter space of Mathieu's equation. Third order wave equations are used to qualitatively describe the effects of phonon-phonon interactions and energy transfer from microwaves to CNTs. This result provides another way to input energy from microwaves to carbon nanotubes besides the usual Joule heating via electron-phonon interaction. This model appears to be the first to point out the role of nonlinear dynamics in the heating of CNTs by microwaves.
- Exploration of hierarchical leadership and connectivity in neural networks in vitro.
- Living neural networks are capable of processing information much faster than a modern computer, despite running at significantly lower clock speeds. Therefore, understanding the mechanisms neural networks utilize is an issue of substantial importance. Neuronal interaction dynamics were studied using histiotypic networks growing on microelectrode arrays in vitro. Hierarchical relationships were explored using bursting (when many neurons fire in a short time frame) dynamics, pairwise neuronal activation, and information theoretic measures. Together, these methods reveal that global network activity results from ignition by a small group of burst leader neurons, which form a primary circuit that is responsible for initiating most network-wide burst events. Phase delays between leaders and followers reveal information about the nature of the connection between the two. Physical distance from a burst leader appears to be an important factor in follower response dynamics. Information theory reveals that mutual information between neuronal pairs is also a function of physical distance. Activation relationships in developing networks were studied and plating density was found to play an important role in network connectivity development. These measures provide unique views of network connectivity and hierarchical relationship in vitro which should be included in biologically meaningful models of neural networks.
- Photoelectric Emission Measurements for CVD Grown Polycrystalline Diamond Films
- We examined CVD grown polycrystalline diamond films having different methane concentrations to detect defects and study the possible correlation between the methane concentration used during the growth process and the defect density. SEM and Raman results show that the amorphous and sp2 carbon content of the films increases with methane concentration. Furthermore, photoelectric emission from diamond is confirmed to be a two-photon process, hence the electrons are emitted from normally unoccupied states. We found that the photoelectric yield, for our samples, decreases with the increase in methane concentration. This trend can be accounted for in two different ways: either the types of defects observed in this experiment decrease in density as the methane concentration increases; or, the defect density stays the same or increases, but the increase in methane concentration leads to an increase in the electron affinity, which reduces the overall photoelectric yield.
- Work Function Study of Iridium Oxide and Molybdenum Using UPS and Simultaneous Fowler-Nordheim I-V Plots with Field Emission Energy Distributions
- The characterization of work functions and field emission stability for molybdenum and iridium oxide coatings was examined. Single emission tips and flat samples of molybdenum and iridium oxide were prepared for characterization. The flat samples were characterized using X-ray Photoelectron Spectroscopy and X-ray diffraction to determine elemental composition, chemical shift, and crystal structure. Flat coatings of iridium oxide were also scanned by Atomic Force Microscopy to examine topography. Work functions were characterized by Ultraviolet Photoelectron Spectroscopy from the flat samples and by Field Emission Electron Distributions from the field emission tips. Field emission characterization was conducted in a custom build analytical chamber capable of measuring Field Emission Electron Distribution and Fowler-Nordheim I-V plots simultaneously to independently evaluate geometric and work function changes. Scanning Electron Microscope pictures were taken of the emission tips before and after field emission characterization to confirm geometric changes. Measurement of emission stability and work functions were the emphasis of this research. In addition, use of iridium oxide coatings to enhance emission stability was evaluated. Molybdenum and iridium oxide, IrO2, were characterized and found to have a work function of 4.6 eV and 4.2 eV by both characterization techniques, with the molybdenum value in agreement with previous research. The analytic chamber used in the field emission analysis demonstrated the ability to independently determine the value and changes in work function and emitter geometry by simultaneous measurement of the Field Emission Energy Distribution and Fowler-Nordheim I-V plots from single emitters. Iridium oxide coating was found to enhance the stability of molybdenum emission tips with a relatively low work function of 4.2 eV and inhibited the formation of high work function molybdenum oxides. However, the method of deposition of iridium and annealing in oxygen to form iridium oxide on molybdenum emitters left rather severe cracking in the protective oxide coating exposing the molybdenum substrate.
- Nuclear Magnetic Resonance in Hydrated Crystals - Potassium Oxalate Monohydrate
- The problem of this study was the measurement of the proton-proton separation in the water molecule of hydration in a single crystal of potassium oxalate monohydrate.
- A Vacuum Tube for an Electrostatic Accelerator
- The purpose of this study has been to design a prototype accelerating tube, to determine the correct point shape and spacing needed to produce corona current along the tube for the case of negative-point-to-positive-plane discharge, and to study the voltage-gradient characteristics of short sections of the tube when they were evacuated to a low internal pressure.
- Magnetic Susceptibility of a Crystalline Free Radical
- The entirety of the investigation discussed in this paper was confined to a study of the spin resonance properties of unpaired electrons of an organic free radical. In the remainder of the paper the theory of electron spin resonance, the apparatus used in the investigation, and the experimental results obtained are discussed in that order.
- Proton Nuclear Magnetic Resonance in Mica
- The experiments to be described here were undertaken for the purpose of determining, if possible, by NMR techniques whether or not the hydroxyl protons in mica are bound in a regular crystalline array, and, if so, whether or not the hydroxyl protons occur in reasonably isolated pairs as in waters of hydration.
- Thermal Properties of a Single Crystal of Bismuth at Liquid-helium Temperatures
- The purpose of this investigation was the determination of the thermal conduction properties of a single crystal of bismuth at liquid-helium temperatures in magnetic fields up to eighteen kilogauss.
- Size Effect in the Electrical Conductivity of Bismuth
- If a physical dimension of a metallic specimen is comparable with, or smaller than, the mean free path of the conduction electrons, then the observed electrical conductivity will be less than that of a conventional bulk sample. This phenomenon is called a size effect, and is the result of electron scattering from the specimen surfaces. In the present investigation, measurements were made on electropolished monocrystalline specimens ranging from matchbox geometry to thick-film geometry in order to obtain further information on the size effect in bismuth at liquid helium temperatures.
- Thermomagnetic Phenomena in Antimony at Liquid Helium Temperatures
- The purpose of this investigation was to study head-transport phenomena in a single crystal of antimony at liquid helium temperatures. In particular, the longitudinal and transverse components of the thermal resistivity tensor were measured as a function of magnetic field up to eighteen kilogauss.
- Approach to Quantum Information starting from Bell's Inequality (Part I) and Statistical Analysis of Time Series Corresponding to Complex Processes (Part II)
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I: Quantum information obeys laws that subtly extend those governing classical information, making possible novel effect such as cryptography and quantum computation. Quantum computations are extremely sensitive to disruption by interaction of the computer with its environment, but this problem can be overcome by recently developed quantum versions of classical error-correcting codes and fault-tolerant circuits. Based on these ideas, the purpose of this paper is to provide an approach to quantum information by analyzing and demonstrating Bell's inequality and by discussing the problems related to decoherence and error-correcting. II: The growing need for a better understanding of complex processes has stimulated the development of new and more advanced data analysis techniques. The purpose of this research was to investigate some of the already existing techniques (Hurst's rescaled range and relative dispersion analysis), to develop a software able to process time series with these techniques, and to get familiar with the theory of diffusion processes.
- An entropic approach to the analysis of time series.
- Statistical analysis of time series. With compelling arguments we show that the Diffusion Entropy Analysis (DEA) is the only method of the literature of the Science of Complexity that correctly determines the scaling hidden within a time series reflecting a Complex Process. The time series is thought of as a source of fluctuations, and the DEA is based on the Shannon entropy of the diffusion process generated by these fluctuations. All traditional methods of scaling analysis, instead, are based on the variance of this diffusion process. The variance methods detect the real scaling only if the Gaussian assumption holds true. We call H the scaling exponent detected by the variance methods and d the real scaling exponent. If the time series is characterized by Fractional Brownian Motion, we have H¹d and the scaling can be safely determined, in this case, by using the variance methods. If, on the contrary, the time series is characterized, for example, by Lévy statistics, H ¹ d and the variance methods cannot be used to detect the true scaling. Lévy walk yields the relation d=1/(3-2H). In the case of Lévy flights, the variance diverges and the exponent H cannot be determined, whereas the scaling d exists and can be established by using the DEA. Therefore, only the joint use of two different scaling analysis methods, the variance scaling analysis and the DEA, can assess the real nature, Gauss or Lévy or something else, of a time series. Moreover, the DEA determines the information content, under the form of Shannon entropy, or of any other convenient entopic indicator, at each time step of the process that, given a sufficiently large number of data, is expected to become diffusion with scaling. This makes it possible to study the regime of transition from dynamics to thermodynamics, non-stationary regimes, and the saturation regime as well. First of all, the efficiency of the DEA is proved with theoretical arguments and with numerical work on artificial sequences. Then we apply the DEA to three different sets of real data, Genome sequences, hard x-ray solar flare waiting times and sequences of sociological interest. In all these cases the DEA makes new properties, overlooked by the standard method of analysis, emerge.
- Complexity as a form of transition from dynamics to thermodynamics: Application to sociological and biological processes.
- This dissertation addresses the delicate problem of establishing the statistical mechanical foundation of complex processes. These processes are characterized by a delicate balance of randomness and order, and a correct paradigm for them seems to be the concept of sporadic randomness. First of all, we have studied if it is possible to establish a foundation of these processes on the basis of a generalized version of thermodynamics, of non-extensive nature. A detailed account of this attempt is reported in Ignaccolo and Grigolini (2001), which shows that this approach leads to inconsistencies. It is shown that there is no need to generalize the Kolmogorov-Sinai entropy by means of a non-extensive indicator, and that the anomaly of these processes does not rest on their non-extensive nature, but rather in the fact that the process of transition from dynamics to thermodynamics, this being still extensive, occurs in an exceptionally extended time scale. Even, when the invariant distribution exists, the time necessary to reach the thermodynamic scaling regime is infinite. In the case where no invariant distribution exists, the complex system lives forever in a condition intermediate between dynamics and thermodynamics. This discovery has made it possible to create a new method of analysis of non-stationary time series which is currently applied to problems of sociological and physiological interest.
- A dynamic and thermodynamic approach to complexity.
- The problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, non-extensive , form of thermodynamics, and another, proposed by the UNT Center for Nonlinear Science, on complexity as a new condition that, for physical systems, would be equivalent to a state of matter intermediate between dynamics and thermodynamics. In the first part of this dissertation, the concept of Kolmogorov-Sinai entropy is introduced. The Pesin theorem is generalized in the formalism of Tsallis non-extensive thermodynamics. This generalized form of Pesin theorem is used in the study of two major classes of problems, whose prototypes are given by the Manneville and the logistic map respectively. The results of these studies convince us that the approach to complexity must be made along lines different from those of the non-extensive thermodynamics. We have been convinced that the Lévy walk can be used as a prototype model of complexity, as a condition of balance between order and randomness that yields new phenomena such as aging, and multifractality. We reach the conclusions that these properties must be studied within a dynamic rather than thermodynamic perspective. The second part focuses on the study of the heart beating problem using a dynamic model, the so-called memory beyond memory, based on the Lévy walker model. It is proved that the memory beyond memory effect is more obvious in the healthy heart beating sequence. The concepts of fractal, multifractal, wavelet transformation and wavelet transform maximum modulus (WTMM) method are introduced. Artificial time sequences are generated by the memory beyond memory model to mimic the heart beating sequence. Using WTMM method, the multifratal singular spectrums of the sequences are calculated. It is clear that the sequence with strong memory beyond memory effect has broader singular spectrum.2003-08
- Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor
- The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the quantum potential is not zero and must be included as part of the quantum kinetic energy for agreement. The numerical data for momentum diffusion of classical kicked rotor is well fit by a power law DNβ in the number of kicks N. In the anomalous momentum diffusion regions due to accelerator modes the exponent β(K) is slightly less than quadratic, except for a slight dip, in agreement with an upper bound (K2/2)N2. The corresponding coefficient D(K) in these regions has three distinct sections, most likely due to accelerator modes with period greater than one. We also show that the local Lyapunov exponent of the classical kicked rotor has a plateau for a duration that depends on the initial separation and then decreases asymptotically as O(t-1lnt), where t is the time. This behavior is consistent with an upper bound that is determined analytically.
- Random growth of interfaces: Statistical analysis of single columns and detection of critical events.
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The dynamics of growth and formation of surfaces and interfaces is becoming very important for the understanding of the origin and the behavior of a wide range of natural and industrial dynamical processes. The first part of the paper is focused on the interesting field of the random growth of surfaces and interfaces, which finds application in physics, geology, biology, economics, and engineering among others. In this part it is studied the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction g. It is argued that the main properties of Kardar-Parisi-Zhang theory are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model. The second part of the paper deals with the efficiency of the diffusion entropy analysis (DEA) when applied to the studies of stromatolites. In this case it is shown that this tool can be confidently used for the detection of complexity. The connection between the two studies is established by the use of the DEA itself. In fact, in both analyses, that is, the random growth of interfaces and the study of stromatolites, the method of diffusion entropy is able to detect the real scaling of the system, namely, the scaling of the process is determined by genuinely random events, also called critical events.
- Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors
- Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's field equation.
- The Concept of Collision Strength and Its Applications
- Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes bimolecular collision reaction rate theory to a reaction rate theory for plasmas. A simple formula of high precision with wide temperature range has been developed for electron impact ionization rates for carbon atoms and ions. The universality of the concept of collision strength is emphasized. This dissertation will show how Arrhenius' chemical reaction rate theory and Thomson's ionization theory can be unified as one single theory under the concept of collision strength, and how many important physical terms in different disciplines, such as activation energy in chemical reaction theory, ionization energy in Thomson's ionization theory, and the Coulomb logarithm in plasma physics, can be unified into a single one -- the threshold value of collision strength. The collision strength, which is a measure of a transfer of momentum in units of energy, can be used to reconcile the differences between Descartes' opinion and Leibnitz's opinion about the "true'' measure of a force. Like Newton's second law, which provides an instantaneous measure of a force, collision strength, as a cumulative measure of a force, can be regarded as part of a law of force in general.
- Complexity as Aging Non-Poisson Renewal Processes
- The search for a satisfactory model for complexity, meant as an intermediate condition between total order and total disorder, is still subject of debate in the scientific community. In this dissertation the emergence of non-Poisson renewal processes in several complex systems is investigated. After reviewing the basics of renewal theory, another popular approach to complexity, called modulation, is introduced. I show how these two different approaches, given a suitable choice of the parameter involved, can generate the same macroscopic outcome, namely an inverse power law distribution density of events occurrence. To solve this ambiguity, a numerical instrument, based on the theoretical analysis of the aging properties of renewal systems, is introduced. The application of this method, called renewal aging experiment, allows us to distinguish if a time series has been generated by a renewal or a modulation process. This method of analysis is then applied to several physical systems, from blinking quantum dots, to the human brain activity, to seismic fluctuations. Theoretical conclusions about the underlying nature of the considered complex systems are drawn.
- Brownian Movement and Quantum Computers
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This problem in lieu of thesis is a discussion of two topics: Brownian movement and quantum computers. Brownian movement is a physical phenomenon in which the particle velocity is constantly undergoing random fluctuations. Chapters 2, 3 and 4, describe Brownian motion from three different perspectives. The next four chapters are devoted to the subject of quantum computers, which are the signal of a new era of technology and science combined together. In the first chapter I present to a reader the two topics of my problem in lieu of thesis. In the second chapter I explain the idea of Brownian motion, its interpretation as a stochastic process and I find its distribution function. The next chapter illustrates the probabilistic picture of Brownian motion, where the statistical averages over trajectories are related to the probability distribution function. Chapter 4 shows how to derive the Langevin equation, introduced in chapter 1, using a Hamiltonian picture of a bath with infinite number of harmonic oscillators. The chapter 5 explains how the idea of quantum computers was developed and how step-by-step all the puzzles for the field of quantum computers were created. The next chapter, chapter 6, discus the basic quantum unit of information namely, the so called qubit and its properties. Chapter 7 is devoted to quantum logic gates, which are important for conducting logic operation in quantum computers. This chapter explains how they were developed and how they are different from classical ones. Chapter 8 is about the quantum algorithm, Shor's algorithm. Quantum algorithm in quantum computers enables one to solve problems that are hard to solve on digital computers. The last chapter contains conclusions on Brownian movement and the field of quantum computers.
- Perturbation of renewal processes
- Renewal theory began development in the early 1940s, as the need for it in the industrial engineering sub-discipline operations research had risen. In time, the theory found applications in many stochastic processes. In this thesis I investigated the effect of seasonal effects on Poisson and non-Poisson renewal processes in the form of perturbations. It was determined that the statistical analysis methods developed at UNT Center for Nonlinear Science can be used to detect the effects of seasonality on the data obtained from Poisson/non-Poisson renewal systems. It is proved that a perturbed Poisson process can serve as a paradigmatic model for a case where seasonality is correlated to the noise and that diffusion entropy method can be utilized in revealing this relation. A renewal model making a connection with the stochastic resonance phenomena is used to analyze a previous neurological experiment, and it was shown that under the effect of a nonlinear perturbation, a non-Poisson system statistics may make a transition and end up in the of Poisson basin of statistics. I determine that nonlinear perturbation of the power index for a complex system will lead to a change in the complexity characteristics of the system, i.e., the system will reach a new form of complexity.
- Emergence of Complexity from Synchronization and Cooperation
- The dynamical origin of complexity is an object of intense debate and, up to moment of writing this manuscript, no unified approach exists as to how it should be properly addressed. This research work adopts the perspective of complexity as characterized by the emergence of non-Poisson renewal processes. In particular I introduce two new complex system models, namely the two-state stochastic clocks and the integrate-and-fire stochastic neurons, and investigate its coupled dynamics in different network topologies. Based on the foundations of renewal theory, I show how complexity, as manifested by the occurrence of non-exponential distribution of events, emerges from the interaction of the units of the system. Conclusion is made on the work's applicability to explaining the dynamics of blinking nanocrystals, neuron interaction in the human brain, and synchronization processes in complex networks.
- Multifunctional Organic-Inorganic Hybrid Nanophotonic Devices
- The emergence of optical applications, such as lasers, fiber optics, and semiconductor based sources and detectors, has created a drive for smaller and more specialized devices. Nanophotonics is an emerging field of study that encompasses the disciplines of physics, engineering, chemistry, biology, applied sciences and biomedical technology. In particular, nanophotonics explores optical processes on a nanoscale. This dissertation presents nanophotonic applications that incorporate various forms of the organic polymer N-isopropylacrylamide (NIPA) with inorganic semiconductors. This includes the material characterization of NIPA, with such techniques as ellipsometry and dynamic light scattering. Two devices were constructed incorporating the NIPA hydrogel with semiconductors. The first device comprises a PNIPAM-CdTe hybrid material. The PNIPAM is a means for the control of distances between CdTe quantum dots encapsulated within the hydrogel. Controlling the distance between the quantum dots allows for the control of resonant energy transfer between neighboring quantum dots. Whereby, providing a means for controlling the temperature dependent red-shifts in photoluminescent peaks and FWHM. Further, enhancement of photoluminescent due to increased scattering in the medium is shown as a function of temperature. The second device incorporates NIPA into a 2D photonic crystal patterned on GaAs. The refractive index change of the NIPA hydrogel as it undergoes its phase change creates a controllable mechanism for adjusting the transmittance of light frequencies through a linear defect in a photonic crystal. The NIPA infiltrated photonic crystal shows greater shifts in the bandwidth per ºC than any liquid crystal methods. This dissertation demonstrates the versatile uses of hydrogel, as a means of control in nanophotonic devices, and will likely lead to development of other hybrid applications. The development of smaller light based applications will facilitate the need to augment the devices with control mechanism and will play an increasing important role in the future.
- Nanoscale Materials Applications: Thermoelectrical, Biological, and Optical Applications with Nanomanipulation Technology
- In a sub-wavelength scale, even approaching to the atomic scale, nanoscale physics shows various novel phenomena. Since it has been named, nanoscience and nanotechnology has been employed to explore and exploit this small scale world. For example, with various functionalized features, nanowire (NW) has been making its leading position in the researches of physics, chemistry, biology, and engineering as a miniaturized building block. Its individual characteristic shows superior and unique features compared with its bulk counterpart. As one part of these research efforts and progresses, and with a part of the fulfillment of degree study, novel methodologies and device structures in nanoscale were devised and developed to show the abilities of high performing thermoelectrical, biological, and optical applications. A single β-SiC NW was characterized for its thermoelectric properties (thermal conductivity, Seebeck coefficient, and figure of merit) to compare with its bulk counterpart. The combined structure of Ag NW and ND was made to exhibit its ability of clear imaging of a fluorescent cell. And a plasmonic nanosture of silver (Ag) nanodot array and a β-SiC NW was fabricated to show a high efficient light harvesting device that allows us to make a better efficient solar cell. Novel nanomanipulation techniques were developed and employed in order to fabricate all of these measurement platforms. Additionally, one of these methodological approaches was used to successfully isolate a few layer graphene.
- The Interactions of Plasma with Low-k Dielectrics: Fundamental Damage and Protection Mechanisms
- Nanoporous low-k dielectrics are used for integrated circuit interconnects to reduce the propagation delays, and cross talk noise between metal wires as an alternative material for SiO2. These materials, typically organosilicate glass (OSG) films, are exposed to oxygen plasmas during photoresist stripping and related processes which substantially damage the film by abstracting carbon, incorporating O and OH, eventually leading to significantly increased k values. Systematic studies have been performed to understand the oxygen plasma-induced damage mechanisms on different low-k OSG films of various porosity and pore interconnectedness. Fourier transform infrared spectroscopy, x-ray photoelectron spectroscopy and atomic force microscopy are used to understand the damage kinetics of O radicals, ultraviolet photons and charged species, and possible ways to control the carbon loss from the film. FTIR results demonstrate that O radical present in the plasma is primarily responsible for carbon abstraction and this is governed by diffusion mechanism involving interconnected film nanopores. The loss of carbon from the film can be controlled by closing the pore interconnections, He plasma pretreatment is an effective way to control the damage at longer exposure by closing the connections between the pores.
- Anderson Localization in Two-Channel Wires with Correlated Disorder: DNA as an Application
- This research studied the Anderson localization of electrons in two-channel wires with correlated disorder and in DNA molecules. It involved an analytical calculation part where the formula for the inverse localization length for electron states in a two-channel wire is derived. It also involved a computational part where the localization length is calculated for some DNA molecules. Electron localization in two-channel wires with correlated disorder was studied using a single-electron tight-binding model. Calculations were within second-order Born-approximation to second-order in disorder parameters. An analytical expression for localization length as a functional of correlations in potentials was found. Anderson localization in DNA molecules were studied in single-channel wire and two-channel models for electron transport in DNA. In both of the models, some DNA sequences exhibited delocalized electron states in their energy spectrum. Studies with two-channel wire model for DNA yielded important link between electron localization properties and genetic information.
- Microstructure and Electronic Structures of Er-Doped Si Nano-particles Synthesized by Vapor Phase Pyrolysis
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Si nanoparticles are new prospective optoelectronic materials. Unlike bulk Si cry-stals, Si nanoparticles display intriguing room-temperature photoluminescence. A major challenge in the fabrication of Si nanoparticles is the control of their size distribution. The rare-earth element Er has unique photo emission properties, including low pumping power, and a temperature independent, sharp spectrum. The emission wavelength matches the transmission window of optical fibers used in the telecommunications industry. Therefore, the study of Er-doped Si nanoparticles may have practical significance. The goals of the research described in this dissertation are to investigate vapor phase pyrolysis methods and to characterize the microstructure and associated defects, particles size distributions and photoluminescence efficiencies of doped and undoped Si nanoparticles using analytical transmission electron microscopy, high resolution electron microscopy, and optical spectroscopy. Er-doped and undoped Si nanoparticles were synthesized via vapor-phase pyrolysis of disilane at Texas Christian University. To achieve monodisperse size distributions, a process with fast nucleation and slow growth was employed. Disilane was diluted to 0.48% with helium. A horizontal pyrolysis oven was maintained at a temperature of 1000 °C. The oven length was varied from 1.5 cm to 6.0 cm to investigate the influence of oven length on the properties of the nanoparticles. The Si nanoparticles were collected in ethylene-glycol. The doped and undoped Si nanoparticles have a Si diamond cubic crystal structure. Neither Er precipitation, Er oxides or Er silicides were detected in any of the samples. The Er dopant concentration was about 2 atom% for doped samples from the 3.0 and 6.0 cm ovens as determined by quantitative analysis using X-ray energy dispersive spectroscopy. The average Si nanoparticle size increases from 11.3 to 15.2 nm in the doped samples and from 11.1 to 15.7 nm in the undoped samples as the oven length increases from 1.5 to 6.0 cm. HREM data show that average Si nanocrystallite size varies from 6.4 to 3.3 to 5.9 nm in the doped samples, and from 7.5 to 12.2 nm in the undoped samples as the oven length increases. Room-temperature Er photoluminescence has been detected near 1.54 :m from all doped samples. Saturation of the Er photoluminescence intensity at large emission power and the monotonic decrease of the intensity as a function of the emission wavelength in the doped sample from the 3.0 cm oven suggest that a carrier-mediated energy transfer process occurs in the Er-doped Si nanoparticles. It is the first time to successfully fabricate and investigate Er-doped Si nanoparticles.
- EEG, Alpha Waves and Coherence
- This thesis addresses some theoretical issues generated by the results of recent analysis of EEG time series proving the brain dynamics are driven by abrupt changes making them depart from the ordinary Poisson condition. These changes are renewal, unpredictable and non-ergodic. We refer to them as crucial events. How is it possible that this form of randomness be compatible with the generation of waves, for instance alpha waves, whose observation seems to suggest the opposite view the brain is characterized by surprisingly extended coherence? To shed light into this apparently irretrievable contradiction we propose a model based on a generalized form of Langevin equation under the influence of a periodic stimulus. We assume that there exist two different forms of time, a subjective form compatible with Poisson statistical physical and an objective form that is accessible to experimental observation. The transition from the former to the latter form is determined by the brain dynamics interpreted as emerging from the cooperative interaction among many units that, in the absence of cooperation would generate Poisson fluctuations. We call natural time the brain internal time and we make the assumption that in the natural time representation the time evolution of the EEG variable y(t) is determined by a Langevin equation perturbed by a periodic process that in this time representation is hardly distinguishable from an erratic process. We show that the representation of this random process in the experimental time scale is characterized by a surprisingly extended coherence. We show that this model generates a sequence of damped oscillations with a time behavior that is remarkably similar to that derived from the analysis of real EEG's. The main result of this research work is that the existence of crucial events is not incompatible with the alpha wave coherence. In addition to this important result, we find another result that may help our group, or any other research group working on the analysis of brain's dynamics, to prove or to disprove the existence of crucial events. We study the diffusion process generated by fluctuations emerging from the same model after filtering out the alpha coherence, and we study the recursion to the origin. We study the survival probability of this process, namely the probability that up to a given time no re-crossing of the origin occurs. We find that this is an inverse power law with a power that depends on whether or not crucial events exist.
- Growing carbon nanotubes by chemical vapor deposition technique.
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Carbon nanotubes were synthesized in the laboratory using chemical vapor deposition at different methane concentration. I found that a methane concentration of 4 sccm was ideal for well recognizable carbon nanotubes. A higher concentration led to fewer nanotube growth and silicon carbide structure. Coating the sample first with Fe(NO3)3 created a catalyst base on the substrate for the nanotube to adhere and grow on.
- Nonlinear UV Laser Build-up Cavity: An Efficient Design
- Using the concept of the build-up cavity for second harmonic generation to produce 243nm laser light, an innovative cavity is theoretically explored using a 15mm length CLBO crystal. In order to limit the losses of the cavity, the number of effective optical surfaces is kept to only four and the use of a MgF2 crystal is adopted to separate the harmonic and fundamental laser beam from each other. The cavity is shown to have an expected round trip loss of five tenths of a percent or better, resulting in a conversion efficiency greater than 65%.
- A Reverberation Time Meter
- This thesis describes the construction of an apparatus to measure reverberation time.
- Studying Interactions of Gas Molecules with Nanomaterials Loaded in a Microwave Resonant Cavity
- A resonant cavity operating in TE011 mode was used to study the adsorption response of single walled carbon nanotubes (SWCNTs) and other nanomaterials for different types of gas molecules. The range of the frequency signal as a probe was chosen as geometry dependent range between 9.1 -9.8 GHz. A highly specific range can be studied for further experiments dependent on the type of molecule being investigated. It was found that for different pressures of gases and for different types of nanomaterials, there was a different response in the shifts of the probe signal for each cycle of gassing and degassing of the cavity. This dissertation suggests that microwave spectroscopy of a complex medium of gases and carbon nanotubes can be used as a highly sensitive technique to determine the complex dielectric response of different polar as well as non-polar gases when subjected to intense electromagnetic fields within the cavity. Also, as part of the experimental work, a range of other micro-porous materials was tested using the residual gas analysis (RGA) technique to determine their intrinsic absorption/adsorption characteristics when under an ultra-high vacuum environment. The scientific results obtained from this investigation, led to the development of a chemical biological sensor prototype. The method proposed is to develop operational sensors to detect toxin gases for homeland security applications and also develop sniffers to detect toxin drugs for law enforcement agency personnel.
- Ion Beam Synthesis of Carbon Assisted Nanosystems in Silicon Based Substrates
- The systematic study of the formation of β-SiC formed by low energy carbon ion (C-)implantation into Si followed by high temperature annealing is presented. The research is performed to explore the optimal annealing conditions. The formation of crystalline β-SiC is clearly observed in the sample annealed at 1100 °C for a period of 1 hr. Quantitative analysis is performed in the formation of β-SiC by the process of implantation of different carbon ion fluences of 1×1017, 2×1017, 5×1017, and 8×1017 atoms /cm2 at an ion energy of 65 keV into Si. It is observed that the average size of β-SiC crystals decreased and the amount of β-SiC crystals increased with the increase in the implanted fluences when the samples were annealed at 1100°C for 1 hr. However, it is observed that the amount of β-SiC linearly increased with the implanted fluences up to 5×1017 atoms /cm2. Above this fluence the amount of β-SiC appears to saturate. The stability of graphitic C-C bonds at 1100°C limits the growth of SiC precipitates in the sample implanted at a fluence of 8×1017 atoms /cm2 which results in the saturation behavior of SiC formation in the present study. Secondly, the carbon cluster formation process in silica and the characterization of formed clusters is presented. Silicon dioxide layers ~500 nm thick are thermally grown on a Si (100) wafer. The SiO2 layers are then implanted with 70 keV carbon ions at a fluence of 5×1017 atoms/cm2. The implanted samples are annealed 1100 °C for different time periods of 10 min., 30 min., 60 min., 90 min., and 120 min., in the mixture of argon and hydrogen gas (96 % Ar + 4% hydrogen). Photoluminescence spectroscopy reveals UV to visible emission from the samples. A detail mechanism of the photoluminescence and its possible origin is discussed by correlating the structural and optical properties of the samples. Raman spectroscopy, X-ray photoelectron spectroscopy, X-ray diffraction, spectroscopy, photoluminescence spectroscopy, and transmission electron microscopy are used to characterize the samples.
- Thorium and Uranium M-shell X-ray Production Cross Sections for 0.4 – 4.0 MeV Protons, 0.4 - 6.0 MeV Helium Ions, 4.5 – 11.3 MeV Carbon Ions, and 4.5 – 13.5 MeV Oxygen Ions.
- The M-shell x-ray production cross section for thorium and uranium have been determined for protons of energy 0.4 - 4.0 MeV, helium ions of energy 0.4 - 6.0 MeV, carbon ions of energy 4.5 - 11.3 MeV and oxygen ions of energy 4.5 - 13.5 MeV. The total cross sections and the cross sections for individual x-ray peaks in the spectrum, consisting of the following transitions Mz (M4-N2, M5-N3, M4-N3), Ma (M5-N6,7), Mb (M4-N6, M5-O3, M4- O2), and Mg (M4-O3, M5-P3, M3-N4, M3-N5), were compared to the theoretical values determined from the PWBA + OBKN and ECUSAR. The theoretical values for the carbon and oxygen ions were also modified to take into account the effects of multiple ionizations of the target atom by the heavier ions. It is shown that the results of the ECUSAR theory tend to provide better agreement with the experimental data.
- Dipole Moments of Diphenyl Compounds with Conjugated Double Bonds
- This thesis is a continuation of a study of molecular moments begun by Joseph T. Fielder. In his paper he discussed the theory and the equipment necessary for such a study. It is the purpose of this paper to set forth modifications of his equipment, to present data obtained with this modified equipment, and to interpret this data.
- The Effect of Average Grain Size on Polycrystalline Diamond Films
- The work function of hydrogen-terminated, polycrystalline diamond was studied using ultraviolet photoelectron spectroscopy. Polycrystalline diamond films were deposited onto molybdenum substrates by electrophoresis for grain sizes ranging from 0.3 to 108 microns. The work function and electron affinity were measured using 21.2 eV photons from a helium plasma source. The films were characterized by x-ray photoelectron spectroscopy to determine elemental composition and the sp2/sp3 carbon fraction. The percentage of (111) diamond was determined by x-ray diffraction, and scanning electron microscopy was performed to determine average grain size. The measured work function has a maximum of 5.1 eV at 0.3 microns, and decreases to 3.2 eV at approximately 4 microns. Then the work function increases with increasing grain size to 4.0 eV at 15 microns and then asymptotically approaches the 4.8 eV work function of single crystal diamond at 108 microns. These results are consistent with a 3-component model in which the work function is controlled by single-crystal (111) diamond at larger grain sizes, graphitic carbon at smaller grain sizes, and by the electron affinity for the intervening grain sizes.
- Carbon nanotube/microwave interactions and applications to hydrogen fuel cells.
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One of the leading problems that will be carried into the 21st century is that of alternative fuels to get our planet away from the consumption of fossil fuels. There has been a growing interest in the use of nanotechnology to somehow aid in this progression. There are several unanswered questions in how to do this. It is known that carbon nanotubes will store hydrogen but it is unclear how to increase that storage capacity and how to remove this hydrogen fuel once stored. This document offers some answers to these questions. It is possible to implant more hydrogen in a nanotube sample using a technique of ion implantation at energy levels ~50keV and below. This, accompanied with the rapid removal of that stored hydrogen through the application of a microwave field, proves to be one promising avenue to solve these two unanswered questions.
- Dipole Moments of Olefenic Diesters
- It is the purpose of this paper to present experimental data for the determination of the dielectric constant and the dipole moments for a series of olefenic diesters of the cis and trans configurations.
- A Deuterium-Deuterium Type Neutron Source
- In view of the advantages of its type, the decision to construct a neutron source of the particle accelerator type was made. The purpose of this thesis is to survey the problems encountered in the construction of the source.
- Absolute Beta Counting Using Thick Sources
- The problem with which we shall concern ourselves in this paper is the self-scattering and self-absorption of beta particles by the source.
- Dipole Moments of Olefinic Esters
- It is the purpose of this thesis to investigate the applicability of the Debye equation to measurements dipole moments of polar compounds in dilute solutions of non-polar solvents more fully than has been done by previous workers at this institution.
- Potential Distribution of an Electrical Source-Sink Combination Along the Axis of an Infinite Cylinder
- In the present paper, an attempt is made to obtain the potential distribution in the case of two such charges, a source-sink combination, located on the axis of a bore hole drilled through an infinite, homogeneous medium.
- Scattering Cross-sections of 4/1 Prolate Spheroids
- This is a report of the second in a projected series of experiments at North Texas State College designed for obtaining information about the microwave scattering properties of various shaped objects.
- The Angular Distribution of the Deuterium-Deuterium Neutrons with 100 Kev Deuterons
- It is the purpose of this paper to present the experimental techniques used in obtaining. 3.25 MeV neutrons from the H2(d,n)He3 reaction, as well as an analysis of the experimental data.